The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 0 X X X X 1 X 1 X 0 0 X 0 X X^2 X X^2 1 X 1 0 1 1 1 1 0 X 0 0 0 0 0 0 0 0 X^2 X X X^2+X 0 X^2+X X^2+X 0 X X^2 X^2+X X^2 X X X^2+X X X^2 X^2+X 0 X^2+X X^2 X^2 X X^2+X 0 X^2+X X^2 0 X^2 X^2+X X^2+X X X 0 0 0 X 0 X^2 X 0 X X^2+X X X^2+X X X^2 X 0 0 X X X^2+X X^2 0 0 0 0 X 0 0 0 0 0 0 0 X^2+X X^2 X X X X 0 X 0 X X^2+X X^2 0 X^2+X X X^2 X^2+X X^2 X^2 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2 X^2+X X^2+X X^2+X X X^2 0 X^2 0 X^2+X X^2 X^2 0 X^2 X X^2 X^2+X 0 X^2+X X^2 X X X^2+X X X 0 X X^2 X 0 0 0 0 X 0 0 0 X X^2+X X X X^2+X 0 X X^2 0 X^2+X X^2+X X^2+X X^2 X^2+X X 0 X^2 X^2+X X^2 X^2+X 0 X^2 X X^2 X X X^2 X^2 X^2+X X^2+X 0 X^2+X X^2 X^2 X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2 X^2+X 0 X X^2 X^2 X X^2 X^2 X X^2 X X 0 X^2+X X X 0 0 0 0 0 X 0 X X X X^2 X X X X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X X X^2+X X^2 X X X^2+X X^2 X 0 0 X^2+X 0 0 X^2+X X^2 X^2 0 X^2 0 X^2 X^2+X X^2 0 0 X X^2+X 0 X X X^2+X X^2 0 X^2 X^2 X^2 X^2 X^2+X X 0 X^2 0 X^2+X X X^2+X 0 0 0 0 0 0 X X X^2 X^2+X X^2+X X X X^2+X 0 X X^2 X^2 X^2 X^2+X X 0 X^2 X^2 0 X^2+X X 0 X^2 X^2+X X^2 X^2 X X X 0 0 X^2 X 0 X X^2+X X^2 X^2 0 0 X X X X^2 X^2+X X^2 0 X^2+X X^2+X X X^2 X 0 X X^2 X^2+X X^2+X X X^2 X^2+X 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+59x^54+84x^55+172x^56+278x^57+332x^58+430x^59+536x^60+770x^61+957x^62+1020x^63+1307x^64+1466x^65+1516x^66+1548x^67+1394x^68+1188x^69+823x^70+642x^71+510x^72+416x^73+310x^74+204x^75+142x^76+96x^77+78x^78+38x^79+34x^80+8x^81+18x^82+2x^83+2x^85+2x^86+1x^94 The gray image is a linear code over GF(2) with n=264, k=14 and d=108. This code was found by Heurico 1.16 in 21.1 seconds.